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# If Pat saved $600 of his earnings last month, how much did Pat earn last month?(1) Pat spent $$\frac{1}{2}$$ of his earnings last month for living expenses and saved $$\frac{1}{3}$$ of the remainder.(2) Of his earnings last month, Pat paid twice as much in taxes as he saved. A Statement (1) alone is sufficient, but statement (2) alone is not sufficient. B Statement (2) alone is sufficient, but statement (1) alone is not sufficient. C Both statements together are sufficient, but neither statement alone is sufficient. D Each statement alone is sufficient. E Statements (1) and (2) together are not sufficient. Solution ## The correct option is C Statement (1) alone is sufficient, but statement (2) alone is not sufficient.Arithmetic Operations with rational numbers Let $$E$$ be Pat's earnings last month. Find a unique value for $$E$$.(1) Pat spent $$\frac{1}{2}E$$ for living expenses and so $$E -\frac{1}{2}E =\frac{1}{2}E$$ remained. Pat saved $$\frac{1}{3}$$ what remained, so Pat saved $$\frac{1}{3}(\frac{1}{2}E) =\frac{1}{6}E$$. But Pat saved$600, so $$600 =\frac{1}{6}E$$ and this gives a unique value for E; SUFFICIENT.(2) Pat saved $600 last month and paid 2($600) in taxes, but there is no way to determine Pat's earnings last month; NOT sufficient.The correct answer is A; statement 1 alone is sufficient.Logical Reasoning

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